Groupes de Lie pseudo-riemanniens plats

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概要

• 論文の詳細を見る

• The determination of affine Lie groups (i.e., which carry a left-invariant affine structure) is an open problem ([12]). In this work we begin the study of Lie groups with a left-invariant, flat pseudo-Riemannian metric (flat pseudo-Riemannian groups). We show that in such groups the left-invariant affine structure defined by the Levi-Civita connection is geodesically complete if and only if the group is unimodular. We also show that the cotangent manifold of an affine Lie group is endowed with an affine Lie group structure and a left-invariant, flat hyperbolic metric. We describe a double extension process which allows us to construct all nilpotent, flat Lorentzian groups. We give examples and prove that the only Heisenberg group which carries a left invariant, flat pseudo-Riemannian metric is the three dimensional one.

• 東北大学の論文

著者

• Medina Alberto

  Departement Des Matematiques Case Courrier 051 Universitede Montpellier Ii

• Aubert Anne

  Departement des Matematiques, Case courrier 051, Universite deMontpellier II

• Aubert Anne

  Departement Des Matematiques Case Courrier 051 Universite Demontpellier Ii

関連論文

• Groupes de Lie pseudo-riemanniens plats

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